C 447 ] 
horizontal parallax, and twice the fine of half the ap- 
parent latitude CG to the fquare of the radius. 
The fine of CE is to the fine of ZC as the fine of 
the horizontal parallax to the radius ; and CE, the dif- 
ference of ZC and ZE, being very fmall, the differ- 
ence of the fines of thofe arches may be efteemed 
to bear to the fine of CE, the ratio of the cofine of 
ZC to the radius ; and thus the difference of the 
fines of ZC and ZE, will be to the fine of ZC as the 
rectangle under the fine of the horizontal parallax and 
the cofine of ZC to the fquare of the radius. And 
in like manner the difference of the fines of ZG and 
ZH, will be to the fine of ZG, as the redtangle under 
the fine of the horizontal parallax and the cofine of 
ZG to the fquare of the radius. But f. ZE is to 
f. ZC as the moon’s horizontaf diameter to her ap- 
parent diameter in C, and f. ZH to f. ZG as the 
moon’s horizontal diameter to her apparent diameter 
in G. Therefore the difference of the apparent 
diameter in G from the apparent diameter in C, is to- 
the horizontal diameter, as the redfangle under the 
fine of the horizontal parallax, and the difference of 
the cofines of ZC and ZG, to the fquare of the, 
radius. But in the triangle CZG, the difference of 
ZC and ZG is lefs than the third fide CG : therefore 
the chord of the difference of thofe arches, and much 
more the difference of their cofines, will be lefs than, 
the chord of CG, or twice the fine of half CG, 
Hence the ratio of the augmentation of the apparent 
diameter in G to the apparent diameter in C, will bc‘ 
lefs than the redfangle under the fine of the horizon^- 
tal parallax and twice the fine of half CG, the appa-c- 
r.cQt latitude, to the fquare of the radius,. 
Morar 
